The Resource Light propagation through biological tissue and other diffusive media : theory, solutions, and software, Fabrizio Martelli ... [et al.], (electronic book)
Light propagation through biological tissue and other diffusive media : theory, solutions, and software, Fabrizio Martelli ... [et al.], (electronic book)
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The item Light propagation through biological tissue and other diffusive media : theory, solutions, and software, Fabrizio Martelli ... [et al.], (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item Light propagation through biological tissue and other diffusive media : theory, solutions, and software, Fabrizio Martelli ... [et al.], (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.
This item is available to borrow from 1 library branch.
 Summary
 This book provides foundational information on modeling light propagation through diffusive media, with special emphasis on biological tissue. A summary of the theoretical background on light propagation through diffusive media is provided with the aid of easytouse software designed to calculate the solutions of the diffusion equation
 Language
 eng
 Extent
 1 online resource (xxii, 274 p. : ill.)
 Note
 "SPIE digital library."
 Contents

 Acknowledgements  Disclaimer  List of Acronyms  List of Symbols  1. Introduction  References
 I. THEORY. 2. Scattering and absorption properties of diffusive media  2.1. Approach followed in this book  2.2. Optical properties of a turbid medium. 2.2.1. Absorption properties; 2.2.2. Scattering properties  2.3. Statistical meaning of the optical properties of a turbid medium  2.4. Similarity relation and reduced scattering coefficient  2.5. Examples of diffusive media  References
 3. The radiative transfer equation and diffusion equation  3.1. Quantities used to describe radiative transfer  3.2. The radiative transfer equation  3.3. The Green's function method  3.4. Properties of the radiative transfer equation. 3.4.1. Scaling properties; 3.4.2. Dependence on absorption  3.5. Diffusion equation. 3.5.1. The diffusion approximation  3.6. Derivation of the diffusion equation  3.7. Diffusion coefficient  3.8. Properties of the diffusion equation. 3.8.1. Scaling properties; 3.8.2. Dependence on absorption  3.9. Boundary conditions. 3.9.1. Boundary conditions at the interface between diffusive and nonscattering media; 3.9.2. Boundary conditions at the interface between two diffusive media  References
 II. SOLUTIONS. 4. Solutions of the diffusion equation for homogeneous media  4.1. Solution of the diffusion equation for an infinite medium  4.2. Solution of the diffusion equation for the slab geometry  4.3. Analytical Green's functions for transmittance and reflectance  4.4. Other solutions for the outgoing flux  4.5. Analytical Green's function for the parallelepiped  4.6. Analytical Green's function for the infinite cylinder  4.7. Analytical Green's function for the sphere  4.8. Angular dependence of radiance outgoing from a diffusive medium  References
 5. Hybrid solutions of the radiative transfer equation  5.1. General hybrid approach to the solutions for the slab geometry  5.2. Analytical solutions of the timedependent radiative transfer equation for an infinite homogeneous medium. 5.2.1. Almost exact timeresolved Green's function of the radiative transfer equation for an infinite medium with isotropic scattering; 5.2.2. Heuristic timeresolved Green's function of the radiative transfer equation for an infinite medium with nonisotropic scattering; 5.2.3. Timeresolved Green's function of the telegrapher equation for an infinite medium  5.3. Comparison of the hybrid models based on the radiative transfer equation and telegrapher equation with the solution of the diffusion equation  References
 6. The diffusion equation for layered media  6.1. Photon migration through layered media  6.2. Initial and boundary value problems for parabolic equations  6.3. Solution of the DE for a twolayer cylinder  6.4. Examples of reflectance and transmittance of a layered medium  6.5. General property of light reemitted by a diffusive medium. 6.5.1. Mean time of flight in a generic layer of a homogeneous Cylinder; 6.5.2. Mean time of flight in a twolayer cylinder; 6.5.3. Penetration depth in a homogeneous medium; 6.5.4. Conclusion  References
 7. Solutions of the diffusion equation with perturbation theory  7.1. Perturbation theory in a diffusive medium and the born approximation  7.2. Perturbation theory: solutions for the infinite medium. 7.2.1. Examples of perturbation for the infinite medium  7.3. Perturbation theory: solutions for the slab. 7.3.1. Examples of perturbation for the slab  7.4. Perturbation approach for hybrid models  7.5. Perturbation approach for the layered slab and for other geometries  7.6. Absorption perturbation by use of the internal pathlength moments  References
 III. SOFTWARE AND ACCURACY OF SOLUTIONS. 8. Software  8.1. Introduction  8.2. The diffusion&perturbation program  8.3. Source code: solutions of the diffusion equation and hybrid models. 8.3.1. Solutions of the diffusion equation for homogeneous media; 8.3.2. Solutions of the diffusion equation for layered media; 8.3.3. Hybrid models for the homogeneous infinite medium; 8.3.4. Hybrid models for the homogeneous slab; 8.3.5. Hybrid models for the homogeneous parallelepiped; 8.3.6. General purpose subroutines and functions  References
 9. Reference Monte Carlo results  9.1. Introduction  9.2. Rules to simulate the trajectories and general remarks  9.3. Monte Carlo program for the infinite homogeneous medium  9.4. Monte Carlo programs for the homogeneous and the layered slab  9.5. Monte Carlo code for the slab containing an inhomogeneity  9.6. Description of the Monte Carlo results reported in the CDROM. 9.6.1. Homogeneous infinite medium; 9.6.2. Homogeneous slab; 9.6.3. Layered slab; 9.6.4. Perturbation due to inhomogeneities inside the homogeneous slab  References
 10. Comparisons of analytical solutions with Monte Carlo results  10.1. Introduction  10.2. Comparisons between Monte Carlo and the diffusion equation: homogeneous medium. 10.2.1. Infinite homogeneous medium; 10.2.2. Homogeneous slab  10.3. Comparison between Monte Carlo and the diffusion equation: homogeneous slab with an internal inhomogeneity  10.4. Comparisons between Monte Carlo and the diffusion equation: layered slab  10.5. Comparisons between Monte Carlo and hybrid models. 10.5.1. Infinite homogeneous medium; 10.5.2. Slab geometry  10.6. Outgoing flux: comparison between Fick and extrapolated boundary partial current approaches  10.7. Conclusions. 10.7.1. Infinite medium; 10.7.2. Homogeneous slab; 10.7.3. Layered slab; 10.7.4. Slab with inhomogeneities inside; 10.7.5. Diffusive media  References
 Appendix A: The first simplifying assumption of the diffusion approximation  Appendix B: Fick's law  Appendix C: Boundary conditions at the interface between diffusive and nonscattering media  Appendix D: Boundary conditions at the interface between two diffusive media  Appendix E: Green's function of the diffusion equation in an infinite homogeneous medium  Appendix F: Temporal integration of the timedependent Green's function  Appendix G: Eigenfunction expansion  Appendix H: Green's function of the diffusion equation for the homogeneous cube obtained with the Eigenfunction method  Appendix I: Expression for the normalizing factor  References  Index
 Isbn
 9780819481832
 Label
 Light propagation through biological tissue and other diffusive media : theory, solutions, and software
 Title
 Light propagation through biological tissue and other diffusive media
 Title remainder
 theory, solutions, and software
 Statement of responsibility
 Fabrizio Martelli ... [et al.]
 Language
 eng
 Summary
 This book provides foundational information on modeling light propagation through diffusive media, with special emphasis on biological tissue. A summary of the theoretical background on light propagation through diffusive media is provided with the aid of easytouse software designed to calculate the solutions of the diffusion equation
 Additional physical form
 Also available in print version.
 Cataloging source
 CaBNvSL
 Dewey number
 535/.3
 Illustrations
 illustrations
 Index
 index present
 LC call number
 QC389
 LC item number
 .L54 2009
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 http://library.link/vocab/relatedWorkOrContributorDate
 1969
 http://library.link/vocab/relatedWorkOrContributorName

 Martelli, Fabrizio
 Society of Photooptical Instrumentation Engineers
 Series statement
 SPIE Press monograph
 Series volume
 193
 http://library.link/vocab/subjectName

 Light
 Tissues
 Target audience
 adult
 Label
 Light propagation through biological tissue and other diffusive media : theory, solutions, and software, Fabrizio Martelli ... [et al.], (electronic book)
 Note
 "SPIE digital library."
 Bibliography note
 Includes bibliographical references and index
 Color
 black and white
 Contents

 Acknowledgements  Disclaimer  List of Acronyms  List of Symbols  1. Introduction  References
 I. THEORY. 2. Scattering and absorption properties of diffusive media  2.1. Approach followed in this book  2.2. Optical properties of a turbid medium. 2.2.1. Absorption properties; 2.2.2. Scattering properties  2.3. Statistical meaning of the optical properties of a turbid medium  2.4. Similarity relation and reduced scattering coefficient  2.5. Examples of diffusive media  References
 3. The radiative transfer equation and diffusion equation  3.1. Quantities used to describe radiative transfer  3.2. The radiative transfer equation  3.3. The Green's function method  3.4. Properties of the radiative transfer equation. 3.4.1. Scaling properties; 3.4.2. Dependence on absorption  3.5. Diffusion equation. 3.5.1. The diffusion approximation  3.6. Derivation of the diffusion equation  3.7. Diffusion coefficient  3.8. Properties of the diffusion equation. 3.8.1. Scaling properties; 3.8.2. Dependence on absorption  3.9. Boundary conditions. 3.9.1. Boundary conditions at the interface between diffusive and nonscattering media; 3.9.2. Boundary conditions at the interface between two diffusive media  References
 II. SOLUTIONS. 4. Solutions of the diffusion equation for homogeneous media  4.1. Solution of the diffusion equation for an infinite medium  4.2. Solution of the diffusion equation for the slab geometry  4.3. Analytical Green's functions for transmittance and reflectance  4.4. Other solutions for the outgoing flux  4.5. Analytical Green's function for the parallelepiped  4.6. Analytical Green's function for the infinite cylinder  4.7. Analytical Green's function for the sphere  4.8. Angular dependence of radiance outgoing from a diffusive medium  References
 5. Hybrid solutions of the radiative transfer equation  5.1. General hybrid approach to the solutions for the slab geometry  5.2. Analytical solutions of the timedependent radiative transfer equation for an infinite homogeneous medium. 5.2.1. Almost exact timeresolved Green's function of the radiative transfer equation for an infinite medium with isotropic scattering; 5.2.2. Heuristic timeresolved Green's function of the radiative transfer equation for an infinite medium with nonisotropic scattering; 5.2.3. Timeresolved Green's function of the telegrapher equation for an infinite medium  5.3. Comparison of the hybrid models based on the radiative transfer equation and telegrapher equation with the solution of the diffusion equation  References
 6. The diffusion equation for layered media  6.1. Photon migration through layered media  6.2. Initial and boundary value problems for parabolic equations  6.3. Solution of the DE for a twolayer cylinder  6.4. Examples of reflectance and transmittance of a layered medium  6.5. General property of light reemitted by a diffusive medium. 6.5.1. Mean time of flight in a generic layer of a homogeneous Cylinder; 6.5.2. Mean time of flight in a twolayer cylinder; 6.5.3. Penetration depth in a homogeneous medium; 6.5.4. Conclusion  References
 7. Solutions of the diffusion equation with perturbation theory  7.1. Perturbation theory in a diffusive medium and the born approximation  7.2. Perturbation theory: solutions for the infinite medium. 7.2.1. Examples of perturbation for the infinite medium  7.3. Perturbation theory: solutions for the slab. 7.3.1. Examples of perturbation for the slab  7.4. Perturbation approach for hybrid models  7.5. Perturbation approach for the layered slab and for other geometries  7.6. Absorption perturbation by use of the internal pathlength moments  References
 III. SOFTWARE AND ACCURACY OF SOLUTIONS. 8. Software  8.1. Introduction  8.2. The diffusion&perturbation program  8.3. Source code: solutions of the diffusion equation and hybrid models. 8.3.1. Solutions of the diffusion equation for homogeneous media; 8.3.2. Solutions of the diffusion equation for layered media; 8.3.3. Hybrid models for the homogeneous infinite medium; 8.3.4. Hybrid models for the homogeneous slab; 8.3.5. Hybrid models for the homogeneous parallelepiped; 8.3.6. General purpose subroutines and functions  References
 9. Reference Monte Carlo results  9.1. Introduction  9.2. Rules to simulate the trajectories and general remarks  9.3. Monte Carlo program for the infinite homogeneous medium  9.4. Monte Carlo programs for the homogeneous and the layered slab  9.5. Monte Carlo code for the slab containing an inhomogeneity  9.6. Description of the Monte Carlo results reported in the CDROM. 9.6.1. Homogeneous infinite medium; 9.6.2. Homogeneous slab; 9.6.3. Layered slab; 9.6.4. Perturbation due to inhomogeneities inside the homogeneous slab  References
 10. Comparisons of analytical solutions with Monte Carlo results  10.1. Introduction  10.2. Comparisons between Monte Carlo and the diffusion equation: homogeneous medium. 10.2.1. Infinite homogeneous medium; 10.2.2. Homogeneous slab  10.3. Comparison between Monte Carlo and the diffusion equation: homogeneous slab with an internal inhomogeneity  10.4. Comparisons between Monte Carlo and the diffusion equation: layered slab  10.5. Comparisons between Monte Carlo and hybrid models. 10.5.1. Infinite homogeneous medium; 10.5.2. Slab geometry  10.6. Outgoing flux: comparison between Fick and extrapolated boundary partial current approaches  10.7. Conclusions. 10.7.1. Infinite medium; 10.7.2. Homogeneous slab; 10.7.3. Layered slab; 10.7.4. Slab with inhomogeneities inside; 10.7.5. Diffusive media  References
 Appendix A: The first simplifying assumption of the diffusion approximation  Appendix B: Fick's law  Appendix C: Boundary conditions at the interface between diffusive and nonscattering media  Appendix D: Boundary conditions at the interface between two diffusive media  Appendix E: Green's function of the diffusion equation in an infinite homogeneous medium  Appendix F: Temporal integration of the timedependent Green's function  Appendix G: Eigenfunction expansion  Appendix H: Green's function of the diffusion equation for the homogeneous cube obtained with the Eigenfunction method  Appendix I: Expression for the normalizing factor  References  Index
 Dimensions
 unknown
 Extent
 1 online resource (xxii, 274 p. : ill.)
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9780819481832
 Other physical details
 digital file.
 Reformatting quality
 access
 Reproduction note
 Electronic resource.
 Specific material designation
 remote
 System details
 System requirements: Adobe Acrobat Reader
 Label
 Light propagation through biological tissue and other diffusive media : theory, solutions, and software, Fabrizio Martelli ... [et al.], (electronic book)
 Note
 "SPIE digital library."
 Bibliography note
 Includes bibliographical references and index
 Color
 black and white
 Contents

 Acknowledgements  Disclaimer  List of Acronyms  List of Symbols  1. Introduction  References
 I. THEORY. 2. Scattering and absorption properties of diffusive media  2.1. Approach followed in this book  2.2. Optical properties of a turbid medium. 2.2.1. Absorption properties; 2.2.2. Scattering properties  2.3. Statistical meaning of the optical properties of a turbid medium  2.4. Similarity relation and reduced scattering coefficient  2.5. Examples of diffusive media  References
 3. The radiative transfer equation and diffusion equation  3.1. Quantities used to describe radiative transfer  3.2. The radiative transfer equation  3.3. The Green's function method  3.4. Properties of the radiative transfer equation. 3.4.1. Scaling properties; 3.4.2. Dependence on absorption  3.5. Diffusion equation. 3.5.1. The diffusion approximation  3.6. Derivation of the diffusion equation  3.7. Diffusion coefficient  3.8. Properties of the diffusion equation. 3.8.1. Scaling properties; 3.8.2. Dependence on absorption  3.9. Boundary conditions. 3.9.1. Boundary conditions at the interface between diffusive and nonscattering media; 3.9.2. Boundary conditions at the interface between two diffusive media  References
 II. SOLUTIONS. 4. Solutions of the diffusion equation for homogeneous media  4.1. Solution of the diffusion equation for an infinite medium  4.2. Solution of the diffusion equation for the slab geometry  4.3. Analytical Green's functions for transmittance and reflectance  4.4. Other solutions for the outgoing flux  4.5. Analytical Green's function for the parallelepiped  4.6. Analytical Green's function for the infinite cylinder  4.7. Analytical Green's function for the sphere  4.8. Angular dependence of radiance outgoing from a diffusive medium  References
 5. Hybrid solutions of the radiative transfer equation  5.1. General hybrid approach to the solutions for the slab geometry  5.2. Analytical solutions of the timedependent radiative transfer equation for an infinite homogeneous medium. 5.2.1. Almost exact timeresolved Green's function of the radiative transfer equation for an infinite medium with isotropic scattering; 5.2.2. Heuristic timeresolved Green's function of the radiative transfer equation for an infinite medium with nonisotropic scattering; 5.2.3. Timeresolved Green's function of the telegrapher equation for an infinite medium  5.3. Comparison of the hybrid models based on the radiative transfer equation and telegrapher equation with the solution of the diffusion equation  References
 6. The diffusion equation for layered media  6.1. Photon migration through layered media  6.2. Initial and boundary value problems for parabolic equations  6.3. Solution of the DE for a twolayer cylinder  6.4. Examples of reflectance and transmittance of a layered medium  6.5. General property of light reemitted by a diffusive medium. 6.5.1. Mean time of flight in a generic layer of a homogeneous Cylinder; 6.5.2. Mean time of flight in a twolayer cylinder; 6.5.3. Penetration depth in a homogeneous medium; 6.5.4. Conclusion  References
 7. Solutions of the diffusion equation with perturbation theory  7.1. Perturbation theory in a diffusive medium and the born approximation  7.2. Perturbation theory: solutions for the infinite medium. 7.2.1. Examples of perturbation for the infinite medium  7.3. Perturbation theory: solutions for the slab. 7.3.1. Examples of perturbation for the slab  7.4. Perturbation approach for hybrid models  7.5. Perturbation approach for the layered slab and for other geometries  7.6. Absorption perturbation by use of the internal pathlength moments  References
 III. SOFTWARE AND ACCURACY OF SOLUTIONS. 8. Software  8.1. Introduction  8.2. The diffusion&perturbation program  8.3. Source code: solutions of the diffusion equation and hybrid models. 8.3.1. Solutions of the diffusion equation for homogeneous media; 8.3.2. Solutions of the diffusion equation for layered media; 8.3.3. Hybrid models for the homogeneous infinite medium; 8.3.4. Hybrid models for the homogeneous slab; 8.3.5. Hybrid models for the homogeneous parallelepiped; 8.3.6. General purpose subroutines and functions  References
 9. Reference Monte Carlo results  9.1. Introduction  9.2. Rules to simulate the trajectories and general remarks  9.3. Monte Carlo program for the infinite homogeneous medium  9.4. Monte Carlo programs for the homogeneous and the layered slab  9.5. Monte Carlo code for the slab containing an inhomogeneity  9.6. Description of the Monte Carlo results reported in the CDROM. 9.6.1. Homogeneous infinite medium; 9.6.2. Homogeneous slab; 9.6.3. Layered slab; 9.6.4. Perturbation due to inhomogeneities inside the homogeneous slab  References
 10. Comparisons of analytical solutions with Monte Carlo results  10.1. Introduction  10.2. Comparisons between Monte Carlo and the diffusion equation: homogeneous medium. 10.2.1. Infinite homogeneous medium; 10.2.2. Homogeneous slab  10.3. Comparison between Monte Carlo and the diffusion equation: homogeneous slab with an internal inhomogeneity  10.4. Comparisons between Monte Carlo and the diffusion equation: layered slab  10.5. Comparisons between Monte Carlo and hybrid models. 10.5.1. Infinite homogeneous medium; 10.5.2. Slab geometry  10.6. Outgoing flux: comparison between Fick and extrapolated boundary partial current approaches  10.7. Conclusions. 10.7.1. Infinite medium; 10.7.2. Homogeneous slab; 10.7.3. Layered slab; 10.7.4. Slab with inhomogeneities inside; 10.7.5. Diffusive media  References
 Appendix A: The first simplifying assumption of the diffusion approximation  Appendix B: Fick's law  Appendix C: Boundary conditions at the interface between diffusive and nonscattering media  Appendix D: Boundary conditions at the interface between two diffusive media  Appendix E: Green's function of the diffusion equation in an infinite homogeneous medium  Appendix F: Temporal integration of the timedependent Green's function  Appendix G: Eigenfunction expansion  Appendix H: Green's function of the diffusion equation for the homogeneous cube obtained with the Eigenfunction method  Appendix I: Expression for the normalizing factor  References  Index
 Dimensions
 unknown
 Extent
 1 online resource (xxii, 274 p. : ill.)
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9780819481832
 Other physical details
 digital file.
 Reformatting quality
 access
 Reproduction note
 Electronic resource.
 Specific material designation
 remote
 System details
 System requirements: Adobe Acrobat Reader
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